Question

the graph of a function $f(x)$ is given below:
select all points which are absolute extrema.
a
b
d
f
g

Explanation:

Step1: Recall the definition of absolute extrema

Absolute maximum is the highest point on the entire graph, and absolute minimum is the lowest point on the entire graph.

Step2: Analyze each point

• Point \(A\): It is not the lowest point as there is point \(F\) which is lower.
• Point \(B\): It is not on the graph of the function \(y = f(x)\).
• Point \(D\): It is a local maximum but not the absolute maximum.
• Point \(F\): It is the lowest point on the entire graph, so it is an absolute minimum.
• Point \(G\): It is the highest point on the entire graph, so it is an absolute maximum.

Answer:

F, G